Fleeting thoughts: A formal and informational definition of ‘context’ and ‘communication’

Prehistory: 

C. S. Piers is who introduced the concept of information as both extension and intension of any semantic unit independently of whether it should be refer to natural semantics (language) or to artificial and formal one. In his semantic theory, sign is both signifier (intension) and signified (extension) thus immediately related to the concept of information, which in turn corresponds to a quantity of signs measurable in the number of elementary signs (such as binary digits, i.e. bits).

Absolutely independently, quantum mechanics generalizes the concept of information as quantum information to be able to reinterpret itself in terms of them. Then quantum information can be thought as replacing the type of elementary signs from bits to qubits, which are as if choices among an infinite set of digits just as bits are those in a set of two digits.

Motivation: 

‘Context’ may be seen as a negative imprint of the text, which in turn can be thought as the intension corresponding to a set of possible contexts, in each of which the text will be relevantly used, therefore representing the extension of a generalized semantic unit defined by the text at issue. Then the pair of a given text and the set of admissible contexts constitutes an extended sign where the text is the signifier and the set of contexts is the signified, measurable in some amount of elementary signs, i.e. by the quantity of information. ‘Communication’ would be the nonempty intersection of ‘text’ and ‘context’.

Thesis:

The transition from binary to quantum information involves communication necessarily.

Arguments:

1. The statement is not more than another interpretation of the fundamental and well-known theorem of S. Kochen and E. Specker (1) in quantum mechanics. Indeed, the utilization of the complex Hilbert space (here represented by the free variable of quantum information) implies necessarily the absence of hidden variables (in the sense of Kochen and Specker, somewhere different of John von Neumann’s (2) ) or the existence of quantum correlations (here represented by formally defined communication).

2. The transition from binary to quantum information involves the concept of communication in a fundamental and physical level and link it to the transition from finiteness to infinity. Both allow of communication to be referred to ontology therefore relating ontology and social ontology, in which the concept of communication is properly used.

3. A semantic approach to quantum mechanics and thus to physics at all seems to appear: Any quantum and therefore physical system may be already interpreted semantically, i.e. as the intension of a semantical and physical unit, to which correspond the set of all possible measurements (all possible contexts of relevance) together with their frequencies of occurrence (use).

Conclusion: 

A generalized situation interpretable in terms of semantics, linguistics, physics, ontology, communication and information theory, etc. is modeled by the complex Hilbert space.

Footnotes:

1 “The Problem of Hidden Variables in Quantum Mechanics,” Journal of Mathematics and Mechanics, 17: 59–87

2 Grundlagen der Quantenmechanik, Springer, 1932, 167-173.